Waves and Light: Superposition and Coherence

Understanding Superposition and Coherence

Superposition is a fundamental principle of wave theory. It states that when two or more waves meet, the resultant displacement at any point is the vector sum of the displacements that the individual waves would cause at that point.
The principle of superposition can lead to interference, which is the production of points of constructive and destructive interference as a result of the superposition of two waves.
Constructive interference occurs when two or more waves are in phase, this results in a wave of greater amplitude.
Destructive interference occurs when two or more waves are in anti-phase, which results in a drop in amplitude to even possible cancellation.
Two light sources are coherent if they emit light waves with a constant phase difference and the same frequency. Coherence is required for clear and sustained interference patterns.

The term path difference is used to refer to the difference in the paths travelled by two waves from their respective sources to the point where they meet.
Constructive interference occurs at a particular point when the path difference between the two waves at that point is a whole multiple of the wavelength.
Destructive interference, on the other hand, occurs when the path difference is an odd multiple of half the wavelength.
The path difference and thus interference pattern can be manipulated by changing the distance between the two sources, the frequency of the waves, and the relative positioning between the sources and the observation point.

Interference of light waves can be observed in everyday phenomena such as the coloured patterns seen on a soap bubble or oil on water.
It’s the interference effect that causes the colours seen in thin film interference.
Using Microwaves in Physics, the interference and diffraction effect can also be observed and measured - the operating wavelength of a microwave is convenient for laboratory investigations.
Principles of superposition and interference have also found use in technologies such as noise-cancelling headphones, sonar, and seismograph imaging.

Normal light sources such as a lamp or the sun produce incoherent light – the light waves emitted are not in phase with each other and are of many different wavelengths.
A laser emits light that is coherent. The photons that make up the light are all in phase with each other and are of a single wavelength.
The coherent nature of laser light makes it ideal for demonstrating and studying interference and diffraction effects.
The study of coherence in light sources forms an essential part of understanding the essential wave-like properties of light that can be observed through interference and diffraction.